The first use of an equals sign, equivalent to 14x+15=71 in modern notation. From The Whetstone of Witte by Robert Recorde (1557).

An equation is a mathematical statement that asserts the equality of two expressions.^[1] In modern notation, this is written by placing the expressions on either side of an equals sign (=), for example

Failed to parse (Missing texvc executable; please see math/README to configure.): x + 3 = 5\,

asserts that x+3 is equal to 5. The = symbol was invented by Robert Recorde (1510–1558), who considered that nothing could be more equal than parallel straight lines with the same length.

Knowns and unknowns[link]

Equations often express relationships between given quantities, the knowns, and quantities yet to be determined, the unknowns. By convention, unknowns are denoted by letters at the end of the alphabet, x, y, z, w, …, while knowns are denoted by letters at the beginning, a, b, c, d, … . The process of expressing the unknowns in terms of the knowns is called solving the equation. In an equation with a single unknown, a value of that unknown for which the equation is true is called a solution or root of the equation. In a set simultaneous equations, or system of equations, multiple equations are given with multiple unknowns. A solution to the system is an assignment of values to all the unknowns so that all of the equations are true.

Types of equations[link]

Equations can be classified according to the types of operations and quantities involved. Important types include:

• An algebraic equation is an equation involving only algebraic expressions in the unknowns. These are further classified by degree.
• A linear equation is an algebraic equation of degree one.
• A polynomial equation is an equation in which a polynomial is set equal to another polynomial.
• A transcendental equation is an equation involving a transcendental function of one of its variables.
• A functional equation is an equation in which the unknowns are functions rather than simple quantities.
• A differential equation is an equation involving derivatives.
• An integral equation is an equation involving integrals.
• A Diophantine equation is an equation where the unknowns are required to be integers.
• A quadratic equation

Identities[link]

One use of equations is in mathematical identities, assertions that are true independent of the values of any variables contained within them. For example, for any given value of x it is true that

Failed to parse (Missing texvc executable; please see math/README to configure.): x (x-1) = x^2-x\,.

However, equations can also be correct for only certain values of the variables.^[2] In this case, they can be solved to find the values that satisfy the equality. For example, consider the following.

Failed to parse (Missing texvc executable; please see math/README to configure.): x^2-x = 0\,.

The equation is true only for two values of x, the solutions of the equation. In this case, the solutions are Failed to parse (Missing texvc executable; please see math/README to configure.): x=0

and Failed to parse (Missing texvc executable; please see math/README to configure.): x=1

.

Many mathematicians^[2] reserve the term equation exclusively for the second type, to signify an equality which is not an identity. The distinction between the two concepts can be subtle; for example,

Failed to parse (Missing texvc executable; please see math/README to configure.): (x + 1)^2 = x^2 + 2x + 1\,

is an identity, while

Failed to parse (Missing texvc executable; please see math/README to configure.): (x + 1)^2 = 2x^2 + x + 1\,

is an equation with solutions Failed to parse (Missing texvc executable; please see math/README to configure.): x=0

and Failed to parse (Missing texvc executable; please see math/README to configure.): x=1

. Whether a statement is meant to be an identity or an equation can usually be determined from its context. In some cases, a distinction is made between the equality sign (Failed to parse (Missing texvc executable; please see math/README to configure.): = ) for an equation and the equivalence symbol (Failed to parse (Missing texvc executable; please see math/README to configure.): \equiv ) for an identity.

Letters from the beginning of the alphabet like a, b, c... often denote constants in the context of the discussion at hand, while letters from the end of the alphabet, like ...x, y, z, are usually reserved for the variables, a convention initiated by Descartes.

Properties[link]

If an equation in algebra is known to be true, the following operations may be used to produce another true equation:

1. Any real number can be added to both sides.
2. Any real number can be subtracted from both sides.
3. Any real number can be multiplied to both sides.
4. Any non-zero real number can divide both sides.
5. Some functions can be applied to both sides. Caution must be exercised to ensure that the operation does not cause missing or extraneous solutions. For example, the equation Failed to parse (Missing texvc executable; please see math/README to configure.): yx=x

has 2 sets of solutions: Failed to parse (Missing texvc executable; please see math/README to configure.): y=1
(with any x) and Failed to parse (Missing texvc executable; please see math/README to configure.): x=0
(with any y). Raising both sides to the exponent of 2 (which means, applying the function Failed to parse (Missing texvc executable; please see math/README to configure.): f(s)=s^2
to both sides of the equation) changes our equation into Failed to parse (Missing texvc executable; please see math/README to configure.): (xy)^2=x^2

, which not only has all the previous solutions but also introduces a new set of extraneous solutions, with Failed to parse (Missing texvc executable; please see math/README to configure.): y=-1

and x being any number.

The algebraic properties (1-4) imply that equality is a congruence relation for a field; in fact, it is essentially the only one.

The most well known system of numbers which allows all of these operations is the real numbers, which is an example of a field. However, if the equation were based on the natural numbers for example, some of these operations (like division and subtraction) may not be valid as negative numbers and non-whole numbers are not allowed. The integers are an example of an integral domain which does not allow all divisions as, again, whole numbers are needed. However, subtraction is allowed, and is the inverse operator in that system.

If a function that is not injective is applied to both sides of a true equation, then the resulting equation will still be true, but it may be less useful. Formally, one has an implication, not an equivalence, so the solution set may get larger. The functions implied in properties (1), (2), and (4) are always injective, as is (3) if we do not multiply by zero. Some generalized products, such as a dot product, are never injective.

More information at Equation solving.

See also[link]

References[link]

External links[link]

• Winplot: General Purpose plotter which can draw and animate 2D and 3D mathematical equations.
• Mathematical equation plotter: Plots 2D mathematical equations, computes integrals, and finds solutions online.
• Equation plotter: A web page for producing and downloading pdf or postscript plots of the solution sets to equations and inequations in two variables (x and y).
• EqWorld—contains information on solutions to many different classes of mathematical equations.
• EquationSolver: A webpage that can solve single equations and linear equation systems.

MF DOOM
MF Doom at the Hultsfred Festival 2011 in Sweden
Background information
Also known as	DOOM, King Geedorah, Metal Face, Metal Fingers, Viktor Vaughn, Zev Love X, Madvillain
Born	(1971-01-09) January 9, 1971 (age 41) London, United Kingdom
Origin	Long Island, New York
Genres	East Coast hip hop
Occupations	Rapper, hip hop producer
Instruments	Vocals, sampler, synthesizer, drum machine, Pro Tools
Years active	1988–1993 1997–present
Labels	Elektra (1988–1993) Sub Verse (1997–2003) Fondle 'Em (1997–2001) Metal Face (1997–present) Big Dada (2003) Naturesounds (2003–present) Rhymesayers (2004) Stones Throw (2004–present) Lex (2005–present)
Associated acts	KMD, Madvillain, Danger Doom, Madlib, MF Grimm, Ghostface Killah, J Dilla, Count Bass D, Aesop Rock, Jneiro Jarel, Gorillaz, Masta Ace, De La Soul
Website	Official website

Daniel Dumile (pronounced /ˈduːmɨleɪ/ DOO-mə-lay; born January 9, 1971) is a hip hop artist who has taken on several stage names in his career, most notably MF Doom, often stylized as MF DOOM, where the "MF" stands for metal face, but metal fingers when using his producing name. He has appeared in several collaborative projects such as Danger Doom (with Danger Mouse) and Madvillain (with Madlib).

History[link]

Early years with KMD[link]

Dumile was born on January 9, 1971, in London, England, the son of a Trinidadian mother and Zimbabwean father.^[1] He then moved with his family to New York and was raised in the city of Long Beach, New York on Long Island.

As Zev Love X, he formed the group KMD in 1988 with his younger brother DJ Subroc and another MC called Rodan. When Rodan left the group, Zev found another MC to replace Rodan named Onyx the Birthstone Kid.^[1] A&R rep Dante Ross learned of KMD through the hip hop group 3rd Bass, and signed the group to Elektra Records.^[2]

Dumile and KMD's recorded debut came on 3rd Bass's song "The Gas Face" from The Cactus Album,^[1] followed in 1991 with KMD's album Mr. Hood, which became a minor hit through its singles "Peachfuzz", "Who Me?" and heavy video play on cable TV's Yo! MTV Raps and Rap City.

Subroc was struck and killed by a car in 1993 while attempting to cross the Long Island Expressway before the release of a second KMD album, titled Black Bastards.^[1] The group was subsequently dropped from Elektra Records that same week. Before the release of the album, it was shelved due to controversy over its cover art,^[2] which featured a cartoon of a stereotypical pickaninny or sambo character being hung from the gallows.

With the loss of his brother, Dumile retreated from the hip hop scene from 1994 to 1997. He testifies to disillusionment and depression, living "damn near homeless, walking the streets of Manhattan, sleeping on benches.^[1][3]" In the late 1990s, he left New York City and settled in Atlanta. According to interviews with Dumile, he was also "recovering from his wounds" and swearing revenge "against the industry that so badly deformed him."^[1] Black Bastards had become bootlegged at the time, leading to Doom's rise in the underground hip hop scene.

Birth of MF DOOM[link]

In 1997, Dumile began freestyling incognito at open-mic events at the Nuyorican Poets Café in Manhattan, obscuring his face by putting a stocking over his head. He meanwhile had taken on a new identity, MF Doom, patterned after and wearing a mask similar to that of Marvel Comics super-villain Doctor Doom, who is depicted rapping on the cover of the 1999 album Operation: Doomsday. He wears this mask while performing and isn't photographed without it, except for very short glimpses in videos such as Viktor Vaughn's "Mr. Clean", "?", and in earlier photos with KMD.^[1] MF Doom's mask has undergone at least one design revision since its adoption (it is now an altered version of the mask worn by the character Maximus Decimus Meridius in the film Gladiator).

Early career[link]

Dumile released three singles on "Bobbito" García's Fondle 'Em Records, "Dead Bent", and "Greenbacks" (1997), and "The M.I.C." (1998). In 1999 Fondle 'Em released MF Doom's first full-length LP, Operation: Doomsday, which included these singles and their b-sides, and additional tracks. Dumile had used the spelling variant "M.F. DOOM" for the singles releases, but thereafter changed this to "MF DOOM".

Among the collaborators on these tracks were fellow members of the Monsta Island Czars collective (The M.I.C.), for which each artist took on the persona of a monster from the Godzilla mythos. Dumile went by the alias "King Geedorah," a three-headed golden dragon space monster, modeled after King Ghidorah, the Toho movie monster who was a three-headed dragon that often battled Godzilla. Some of his appearances on the LP are as, and are credited to this persona, instead of that of MF Doom. Dumile would revisit this character later under various name-spellings.

Guest appearances, production, and instrumental work[link]

In the years intervening before his next full-length solo release, and continually since, Dumile has appeared on several tracks on other artists' LPs and remixes, contributed one-off tracks to compilations, and done various guest production work.^[4]

In 2002, he appeared on the Sound-Ink's Colapsus collection,on a very hard to find track titled "Monday Nite at Fluid" featuring Kurious with production by King Honey, who also produced some tracks for Dumile's album Vaudeville Villain. DOOM also made an appearance in "November Has Come", a track on Gorillaz's 2005 album Demon Days, which reached #6 on the Billboard 200.^[5]

Besides the Viktor Vaughn album Dumile produces all the instrumentation tracks for his solo releases with very few exceptions.^[4]

Beginning in 2001, under the "Metal Fingers" moniker, Dumile began releasing his Special Herbs instrumentals series. Many of these beats can be heard as the instrumentation tracks throughout his body of work. A separate website catalogs for which tracks each instrumental has been used.^[6]

Ongoing career[link]

In 2003, Dumile released the King Geedorah album Take Me to Your Leader. Geedorah is credited as producer, but only appears as an MC on four tracks. The majority of vocal tracks feature guest MCs, and the album features several instrumental montages of sampled vocals from old movies and TV shows—a technique employed on most of Dumile's albums. Both Venomous Villain and Take Me to Your Leader feature appearances by MF Doom.

Also in 2003, Dumile released the LP Vaudeville Villain under the moniker Viktor Vaughn (another play on Doctor Doom, whose "real name" is Victor von Doom). In 2004 he released a follow-up LP, Venomous Villain (also called VV2).

And, in 2004, the second MF Doom album MM.. Food was released by the Minnesota-based label Rhymesayers Entertainment.

Mainstream recognition[link]

DOOM's first commercial breakthrough came in 2004, with the album Madvillainy, created with producer Madlib under the group name Madvillain. Released by Stones Throw Records, the album was a critical and commercial success. MF DOOM was seen by mainstream audiences for the first time as Madvillain received publicity and acclaim in publications such as Rolling Stone, The Washington Post, The New York Times, The New Yorker, and Spin. A video for "All Caps" and a four-date U.S. tour followed the release of Madvillainy. Additional videos for "Rhinestone Cowboy" and "Accordion", both directed by Andrew Gura, were released on the DVDs Stones Throw 101 and Stones Throw 102: In Living the True Gods, respectively.

MF Doom collaborated with Danger Mouse who together are known as DANGERDOOM.

Though still an independent artist, MF DOOM took a bigger step towards the mainstream in 2005 with The Mouse and the Mask, a collaboration with producer DJ Danger Mouse under the group name Danger Doom. The album, released on October 11, 2005 by Epitaph, was done in collaboration with Cartoon Network's Adult Swim and featured voice-actors and characters from its programs (mostly Aqua Teen Hunger Force). Danger Doom reached #41 on the Billboard 200.^[7] In 2006 DOOM hosted the Adult Swim Christmas special and he could be seen in between shows, usually talking about what was up next, and making jokes.

2006–2009[link]

MF Doom produced tracks for both of Ghostface Killah's 2006 albums Fishscale and More Fish, and the two are currently at work on a collaboration album titled Swift & Changeable. So far only track released from the album is "Angels", which appeared on a Nature Sounds compilation in late 2006, and later re-released in a different fashion on Doom's 2009 album Born Like This. Doom has also revealed plans for a second Madvillain album with producer Madlib, with one song, "Monkey Suite", first appearing on the Adult Swim/Stones Throw Records album Chrome Children, later it appeared on Madvillainy 2 - The Madlib Remix. Other potential projects mentioned by Doom include new albums from Danger Doom,^[8] KMD, as well as further albums under both his Viktor Vaughn and King Geedorah aliases. However, many such Doom projects have been rumored in recent years without materializing.

Despite no new Doom releases in 2006, Kidrobot and Stones Throw released an 8" tall Madvillain toy available to coincide with the release of the Chrome Children CD/DVD (hosted by Peanut Butter Wolf) which featured a DVD performance of Madvillain and several other Stones Throw artists. Doom also continued to work with Adult Swim doing voice-over work as Sherman the Giraffe on Perfect Hair Forever, being the voice for The Boondocks ads and previews and hosting their Christmas Eve 2006 programming.

In late January 2009, Lex records confirmed Doom's new album title to be Born Like This, and that the "MF" would be dropped from his name, now just "DOOM".^[9] The album was released worldwide on March 24, 2009.^[10] As a teaser, the track "Ballskin" was posted on Doom's Myspace page on January 13, 2009.^[11] Snippets of the entire album were made available for streaming on Doom's Myspace on the album's release date. The title for the album was inspired by the poem "Dinosauria, We" by poet and writer Charles Bukowski. Doom samples a performance of the poem by Bukowski on the track "Cellz". Previously, Doom used a Bukowski sample for a vocal interlude on 2004's "All Outta Ale.^[12] "Thom Yorke of Radiohead remixed the track "Gazillion Ear" which is available as an iTunes-only bonus track.^[13] June 26, 2009 Kurious released II which featured Doom on the song "Benetton".^[14]

2009-2012[link]

On May 26, 2010, the second single for the next Madvillain album "Paper Mill" was released through Adult Swim.^[15] Expektoration, a live Doom album, was released on September 14, 2010 through Gold Dust Media. In mid 2010, DOOM released the mix-tape "DOOM!", a collection of greatest hits, B-sides and rareties, including the theme for the video game Grand Theft Auto: Chinatown Wars featuring Ghostface Killah, and Biochemical Equation, featuring the RZA.

On July 27, 2011 DOOM and Ghostface Killah released the track "Victory Laps" from their long awaited collaboration project Swift & Changeable on the Nature Sounds label.

DOOM was chosen by Portishead to perform at the ATP I'll Be Your Mirror festival that they curated in July 2011 at London's Alexandra Palace.^[16]

DOOM will be the guest curator for Chapter 48 of Frank151's quarterly magazine. Chapter 48 will be released Summer 2012 and will feature a candid interview with DOOM on a variety of topics.^[17]

In September DOOM will be performing live as part of Bestival 2012 on the Isle Of Wight.^[18]

Live show controversy[link]

Dumile has become infamous for allegedly sending imposters to perform on his behalf.^[19] Doom initially countered such accusations by claiming that he lost weight and thus looked - and sounded - different,^[20] before his road manager described the move as an intentional choice made by Dumile.^[21] For his 2011 UK tour, a promoter for the Glasgow show - fearing reduced attendance from a cautious public - guaranteed on Twitter that Dumile would be appearing in person.

Discography[link]

Solo[link]

• 1999: Operation: Doomsday
• 2003: Take Me to Your Leader (as King Geedorah)
• 2003: Vaudeville Villain (as Viktor Vaughn)
• 2004: Venomous Villain (as Viktor Vaughn)
• 2004: Mm.. Food
• 2009: Born Like This (as DOOM)

Compilation Albums[link]

• 2009: Unexpected Guests

Collaboration Albums[link]

• 1991: Mr. Hood (as Zev Love X with KMD)
• 2001: Black Bastards (as Zev Love X with KMD)
• 2003: Escape from Monsta Island! (as King Geedorah with Monsta Island Czars)
• 2004: Madvillainy (with Madlib as Madvillain)
• 2005: The Mouse and the Mask (with Danger Mouse as DANGERDOOM)
• 2006: Occult Hymn (with Danger Mouse as DANGERDOOM)
• 2012: Son of Yvonne (with Masta Ace as MA DOOM)
• 2012: Key to the Kuffs (with Jneiro Jarel as JJ DOOM) ^[22]
• TBA: Swift & Changeable (with Ghostface Killah as DOOMSTARKS)

References[link]

External links[link]

Wikiquote has a collection of quotations related to: Daniel Dumile

• MF Doom on Myspace
• Official website

Jill Tarter
Tarter at TED. Photograph by Steve Jurvetson.
Born	(1944-01-16) January 16, 1944 (age 68)
Nationality	United States
Alma mater	University of California at Berkeley Cornell University
Occupation	Astronomer

Jill Cornell Tarter (born Jan 16, 1944) is an American astronomer and the outgoing director of the Center for SETI Research, holding the Bernard M. Oliver Chair for SETI at the SETI Institute.^[1]

Education[link]

Tarter received her undergraduate education at Cornell University, where she earned a Bachelor of Engineering Physics Degree, and a Master's degree and PhD in astronomy from the University of California at Berkeley.^[2]

Astronomy career[link]

Tarter has worked on a number of major scientific projects, most relating to the search for extraterrestrial life. As a graduate student, she worked on the radio-search project SERENDIP, and created the corresponding backronym, "Search for Extraterrestrial Radio Emissions from Nearby Developed Intelligent Populations." She was project scientist for NASA's High Resolution Microwave Survey (HRMS) in 1992 and 1993 and subsequently director of Project Phoenix (HRMS reconfigured) under the auspices of the SETI Institute. She was co-creator with Margaret Turnbull of the HabCat in 2002, a principal component of Project Phoenix. Tarter has published dozens of technical papers and lectures extensively both on the search for extraterrestrial intelligence and the need for proper science education. She is credited with coining the term "brown dwarf" for the classification of stars with insufficient mass to sustain hydrogen fusion.^[3] She has spent 35 years in the quest for extraterrestrial life and announced her retirement in 2012.^[1]

Honors and awards[link]

Tarter's work in astrobiology and her success as a female scientist have garnered achievement awards from several scientific organizations.

• Awarded a Lifetime Achievement Award by Women in Aerospace in 1989.
• Received two public service medals from NASA.^[4]
• Was elected a Fellow of the American Association for the Advancement of Science in 2002 and a Fellow of the California Academy of Sciences in 2003.
• Received the Adler Planetarium Women in Space Science Award in 2003.
• Was awarded the Telluride Tech Festival Award of Technology in 2001.^[5]
• Was named one of the 100 most influential people in the world by Time Magazine in 2004.^[6]
• Received Wonderfest's Carl Sagan Prize for Science Popularization in 2005.^[7]
• Recipient of a 2009 TED Prize.^[8][9]
• Elected a Fellow of the Committee for Skeptical Inquiry.^[10]

In popular culture[link]

Tarter's astronomical work is illustrated in Carl Sagan's novel Contact. In the film version of Contact, the protagonist Ellie Arroway is played by Jodie Foster. Tarter conversed with the actress for months before and during filming, and Arroway was "largely based" on Tarter's work.^[2] She has also been featured in John Boswell's Symphony of Science music video, "The Poetry of Reality (An Anthem for Science)".^[11]

References[link]

External links[link]

• Lecture about long-term SETI strategies presented to the Long Now Foundation (Ogg Vorbis format).
• Finding intelligent life with telescopes and computers, podcast 2008.
• Talk entitled "Why the search for alien intelligence matters", presented at the TED2009 conference
• Interview posted at the TED Blog
• A brief bio
• Profile of Jill Tarter, in COSMOS magazine